Question: The sum of two numbers is $86$, and their difference is $10$. What are the two numbers?
Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 86}$ ${x-y = 10}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 96 $ $ x = \dfrac{96}{2} $ ${x = 48}$ Now that you know ${x = 48}$ , plug it back into $ {x+y = 86}$ to find $y$ ${(48)}{ + y = 86}$ ${y = 38}$ You can also plug ${x = 48}$ into $ {x-y = 10}$ and get the same answer for $y$ ${(48)}{ - y = 10}$ ${y = 38}$ Therefore, the larger number is $48$, and the smaller number is $38$.